A dynamics cart carrying a black 10.0 cm strip accelerates uniformly and passes through two photogates. The time for the strip through the first photogate, time in Gate1, is 0.250 s and through the second photogate, time in Gate2, is 0.180 s.
(1) Determine the average velocity of the cart as the stripe passes through the first photogate.
(2) Determine the instantaneous velocity of the cart at the middle of this time
interval.
(3) Based on your answers to question 1 and 2, at what time is the average velocity equal to the instantaneous velocity?
To answer these questions, we need to calculate the average velocity and instantaneous velocity using the given data. Let's break it down step by step.
(1) To determine the average velocity of the cart as the stripe passes through the first photogate, we need to use the formula:
Average velocity = displacement / time
Since the problem doesn't provide the displacement, we can assume that the strip passes through the two photogates in a straight line.
Therefore, the displacement between the two photogates is the length of the strip, which is given as 10.0 cm.
Now, we can calculate the average velocity:
Average velocity = 10.0 cm / 0.250 s
Note: To make the units consistent, we can convert centimeters to meters:
1 meter = 100 centimeters.
So, 10.0 cm = 10.0 cm / 100 = 0.1 meters.
Average velocity = 0.1 m / 0.250 s = 0.4 m/s.
Therefore, the average velocity of the cart as the stripe passes through the first photogate is 0.4 m/s.
(2) To determine the instantaneous velocity of the cart at the middle of the time interval, we consider that the initial velocity and final velocity are the same during uniform acceleration.
So, the instantaneous velocity at the middle of the time interval is equal to the average velocity.
Hence, the instantaneous velocity is also 0.4 m/s.
(3) The average velocity will be equal to the instantaneous velocity when the object undergoes constant velocity. In other words, when the acceleration is zero.
Since the cart is accelerating uniformly, the instantaneous and average velocities will not be the same at any specific time during the interval.
Therefore, there is no time at which the average velocity is equal to the instantaneous velocity.
To summarize:
(1) The average velocity of the cart as the stripe passes through the first photogate is 0.4 m/s.
(2) The instantaneous velocity of the cart at the middle of the time interval is also 0.4 m/s.
(3) There is no time when the average velocity is equal to the instantaneous velocity in this scenario.